That seems odd to me. I don't think I've read any ring/algebra/module theory text that doesn't explicitly denote equivalence classes with, for example, square brackets.
There's a canonical ring homomorphism from the integers into any commutative ring with 1. When such a homomorphism is unique, you often omit it, hence mathematicians sometimes just write numbers without equivalence class brackets.
This is not limited to rings of the form Z/nZ.